Show the Proof

import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof

	step type	requirements	statement
0	instantiation	1, 2, 3, 4, 5*	, ,  ⊢
	: , : , : , : , :
1	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled
2	instantiation	6, 12	⊢
	:
3	instantiation	14, 7, 8	,  ⊢
	: , : , :
4	reference	31	⊢
5	instantiation	9, 31, 10*	⊢
	: , :
6	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
7	instantiation	11, 12, 13	⊢
	: , : , :
8	instantiation	14, 15, 16	,  ⊢
	: , : , :
9	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
10	instantiation	17, 31, 39, 18*, 19*	⊢
	: , : , :
11	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
12	theorem		⊢
	proveit.numbers.numerals.decimals.posnat9
13	instantiation	20, 36	⊢
	: , :
14	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
15	instantiation	21, 25, 22, 43, 23*	⊢
	: , : , :
16	instantiation	24, 25, 26, 40, 27, 28, 29	,  ⊢
	: , : , : , :
17	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
18	instantiation	30, 31	⊢
	:
19	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
20	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
21	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_cart_exps_within_cart_exp
22	instantiation	32	⊢
	: , :
23	theorem		⊢
	proveit.numbers.numerals.decimals.mult_3_3
24	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
25	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
26	instantiation	32	⊢
	: , :
27	instantiation	32	⊢
	: , :
28	assumption		⊢
29	modus ponens	33, 34	⊢
30	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
31	instantiation	35, 36, 37	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
33	instantiation	38, 39, 40	⊢
	: , : , : , : , : , :
34	generalization	41	⊢
35	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
36	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
37	assumption		⊢
38	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
39	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
40	instantiation	42, 43	⊢
	:
41	assumption		⊢
42	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
43	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
*equality replacement requirements